28/08/2020

On the Science & Math Blog, why wear a mask?

Foto: Rovena Rosa/Agência Brasil

Reproduction from the IMPA Science & Mathematics blog, from O Globo, coordinated by Claudio Landim.

Paulo A. Maia Neto, professor at the Institute of Physics – UFRJ

How to write about basic physics in the midst of the worst pandemic in decades? Here we will see how physics provides the essential elements for understanding an important mechanism of Covid-19 contagion.

In this article, we are interested in very small droplets, with sizes ranging from hundreds of nanometers to a few microns. Let's look at some definitions: 1 micron represents one thousandth of a millimeter, while a nanometer represents one thousandth of a micron. A strand of hair has a diameter of about 100 microns or slightly smaller, depending on the person. The size of bacteria is typically on the order of 1 micron. Bacteria and other biological cells are too small to be seen with the naked eye, but they can be observed with the aid of an optical microscope.

Similarly, the micro and nano-droplets of bodily fluid expelled when breathing are invisible to the naked eye. Yet, they provide an important mechanism of contagion [1]. In fact, invisible droplets carry the SARS-CoV-2 coronavirus from a patient with Covid-19 directly to the respiratory tract of another person, causing infection.

Because they are so small, droplets in the hundreds of nanometers range behave very differently from macroscopic drops. For example, the movement of raindrops, which are about a millimeter or larger in size, is determined primarily by the Earth's gravitational attraction. Compared to a raindrop, the volume of a micrometric droplet is a billion times smaller. Consequently, its mass will also be approximately a billion times smaller, making the gravitational attraction negligible. Instead of falling like a raindrop, a droplet of hundreds of nanometers remains suspended in the ambient air, performing an erratic movement, because its tiny mass makes it very sensitive to collisions with the molecules that make up the air.

Liquid or solid particles suspended and dispersed in a gas are called aerosols. Because they are very small (sub-micrometer size), they perform erratic motion, called Brownian motion, as illustrated by the trajectory shown in the figure below [2].

Unlike the ballistic motion of a macroscopic droplet, the motion of aerosols is probabilistic, resulting from a huge number of uncontrolled collisions with gas molecules.

In poorly ventilated environments, aerosols hundreds of nanometers in size remain suspended in the ambient air for several hours, performing random movements that easily bypass face shields or masks that are poorly fitted to the face.

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